Implementing a Kalman filter for position, velocity, acceleration

I've used Kalman filters for various things in the past, but I'm now interested in using one to track position, speed and acceleration in the context of tracking position for smartphone apps. It strikes me that this should be a text book example of a simple linear Kalman filter, but I can't seem to find any online links which discuss this. I can think of various ways of doing this, but rather than researching it from scratch, perhaps someone here can point me in the right direction:

1. Does anyone know the best way of setting up this system? For example, given the recent history of position observations, what's the best way of predicting the next point in the Kalman filter state space? What are the advantages and disadvantages of including acceleration in the state space? If all measurements are position, then if speed and acceleration are in the state space can the system become unstable? Etc ...


2. Alternatively, does anyone know of a good reference for this application of Kalman filters?

Thanks

Answer

This is the best one that I know of

Full derivation with explanation

Kalman

This is a good resource for learning about the Kalman filter. If you are more concerned with getting the smartphone app working I would suggest looking for a pre-existing implementation of the Kalman filter. Why reinvent the wheel? For example if you are developing for android, openCV has an implementation of the Kalman filter. See Android OpenCV

Bradski and Kaehler is a good resource on image processing in general and includes a section on the Kalman filter including code examples.